Impacts of Heat Decarbonisation on System Adequacy considering Increased Meteorological Sensitivity
Matthew Deakin, Hannah Bloomfield, David Greenwood, Sarah Sheehy, Sara Walker, Phil C. Taylor
IImpacts of Heat Decarbonisation on System Adequacyconsidering Increased Meteorological Sensitivity
Matthew Deakin a, , Hannah Bloomfield b , David Greenwood a , Sarah Sheehy c ,Sara Walker a , Phil C. Taylor d a Newcastle University, Newcastle-upon-Tyne, UK b University of Reading, Reading, UK c Durham University, Durham, UK d University of Bristol, Bristol, UK
Abstract
This paper explores the impacts of decarbonisation of heat on demand andsubsequently on the generation capacity required to secure against system ad-equacy standards. Gas demand is explored as a proxy variable for modellingthe electrification of heating demand in existing housing stock, with a focus onimpacts on timescales of capacity markets (up to four years ahead). The workconsiders the systemic changes that electrification of heating could introduce, in-cluding biases that could be introduced if legacy modelling approaches continueto prevail. Covariates from gas and electrical regression models are combined toform a novel, time-collapsed system model, with demand-weather sensitivitiesdetermined using lasso-regularized linear regression. It is shown, using a GBcase study with one million domestic heat pump installations per year, thatthe sensitivity of electrical system demand to temperature (and subsequentlysensitivities to cold/warm winter seasons) could increase by 50% following fouryears of heat demand electrification. A central estimate of 1.75 kW additionalpeak demand per heat pump is estimated, with variability across three pub-lished heat demand profiles leading to a range of more than 14 GW in the mostextreme cases. It is shown that the legacy approach of scaling historic demand,as compared to the explicit modelling of heat, could lead to over-procurementof 0.79 GW due to bias in estimates of additional capacity to secure. Failure toaddress this issue could lead to £ Keywords:
Capacity adequacy, heat decarbonisation, energy systemtransitions, energy meteorology, capacity markets.
1. Introduction
Capacity markets have become a common framework for providing securityof supply in energy systems without problems of oversupply of costly peakingcapacity or the high economic and political costs of load shedding. Peak elec-tricity demands are expected to grow significantly in regions with high levels of
Preprint submitted to Elsevier February 23, 2021 a r X i v : . [ s t a t . A P ] F e b as-fueled space heating, as heat is moved onto electrical systems to meet de-carbonisation targets. These heat demands have much stronger sensitivities tometeorological and seasonal factors than historic electrical demand [1, 2, 3, 4].In some countries this issue is compounded by the replacement of aging con-ventional thermal plant by renewable generation which is highly sensitive tometeorological conditions [5, 3]. The study of system adequacy uses probabilis-tic methods, and demand uncertainty can both bias and increase variability inthe estimates of capacity to secure; this bias should therefore be identified and,wherever possible, minimized. In fact, it is the range of calculated capacity tosecure values across scenarios that sets the procurement target in some markets[6]. Given the large sums allocated in the capacity market ( £
700 million in themost recent GB capacity auction), even modest reductions in uncertainty couldyield significant dividends in terms of social welfare.Despite this, the consideration of uncertainty in underlying changes in de-mand on system adequacy is seldom considered in detail. The system adequacyliterature of the past decade has primarily focused on the determination of ca-pacity value of non-dispatchable plant (e.g., renewables, demand-side response,energy storage) [7, 8, 9, 10, 11, 12, 13, 14]. These approaches assume a known,well-defined distribution of demand, with approaches typically scaling historicdemand curves to meet projected forecast peak demand [6], neglecting changesin the distribution of demand duration curves that may occur due to clean en-ergy transitions. To address this, a recent review of GB capacity market byindependent academic experts made the formal recommendation that this issuebe explored, noting that ‘The factors affecting the evolution of peak behaviourshould be analysed ... from the broad perspectives of current and future techni-cal, society and regulatory evolutions’ [15]. This point is particularly pertinentgiven recent annual heat pump installation targets of 600,000 and one millionper year (by the close of this decade) which have been proposed by the UK gov-ernment and UK’s Climate Change Committee, respectively; this will increasedemand-weather sensitivity dramatically [16].Although there are a range of capacity market designs and time frames, itis generally the case that the most important timescale for capacity markets istypically between τ − τ − • Changes in demand-weather sensitivity.
The evolution of demand-weathersensitivities are studied using Lasso-Regularized linear regression. Weather3ariables known to correlate with either gas or electricity demand arestudied comprehensively, with the covariates subsequently derived fromclimate reanalysis data. • Bias arising from the legacy Load Duration Curve approach.
Models ac-counting for heat demand explicitly are compared against the legacy ap-proach whereby heat demand growth is implied by the scaling of historicdemand. Possible biases introduced by the legacy implicit approach arequantified. • Estimating scenario variability in Additional Capacity to Secure.
Scenarioanalysis is used to capture possible changes in variability of capacity tosecure, with meteorological sensitivities and heat demand profile uncer-tainties considered.By considering a detailed system adequacy model with these objectives in mind,we study not only the effects of heat pumps on demand, but also how theyinfluence the capacity required to meet security of supply standards.The contributions of the work are summarised as follows.1. A demand model is proposed that explicitly accounts for increased electri-cal space heating demand at a national level, and is suitable for considera-tion within system adequacy studies. Space heating demand is estimatedby assimilation of historical gas demand data with heat pump usage pro-files.2. The demand model is considered alongside 30 years of historic climatereanalysis data to create a demand hindcast covering winters from 1990to 2020. The model uses Lasso-Regularized regression to avoid overfittingand exclude uninformative covariates. Net demand across each winter canthen be hindcast using coincident renewable generation.3. The model of net demand is combined with models of conventional andrenewable generation to quantify security of supply in terms of loss ofload expectation and subsequently capacity to secure for a GB case study.Scenario analysis across heat pump profiles and coefficients of performanceshow variability in capacity to secure greater than all scenarios presentlyconsidered in the most recent GB capacity market auction.4. It is demonstrated for the first time that significant bias in capacity tosecure could be introduced if models fail to capture changes in the un-derlying end-uses of electrical demand. This is achieved by comparingthe explicit space heating model with conventional approaches that ignorechanges in time- and weather-based dependencies of electrified heatingdemand.This paper has the following structure. Firstly, the novel Explicit heatingmodel is introduced in Section 2, to illustrate how heating demand can beaccounted for in time-collapsed adequacy models in a natural way. In Section3, we outline the Lasso-based linear regression approach, used to consider howheating demand could change the nature of future demand curves. The specific4 istoric systemdemand Linear regression Renewable portfolio
Dispatchable generation X System margin
Z = X + Y – D
Caculate LOLEand ACTSNet demand hindcast
D – Y
Weather data(reanalysis) E , G NDM
Figure 1: High-level modelling approach. The net demand D − Y is calculated for a given yearby combining a linear model of historic system electrical and Non Daily Metered (NDM) gasdemand E, G
NDM with coincident renewable generation Y . This is combined with dispatch-able generation X , from which Loss of Load Expectation (LOLE) and Additional Capacity toSecure (ACTS) can be calculated. The NDM gas demand is used as a proxy for space heatingdemand. details of the GB system model are outlined in Section 4, to introduce the keycharacteristics of the subsequent detailed case study. In Section 5, the full casestudy is used to study the key impacts of increased sensitivity, bias in capacityto secure estimates, and increased variability in capacity to secure. Salientconclusions on the modelling approach are drawn in Section 6.
2. Time-Collapsed System Adequacy Modelling
A energy system is adequate at a given time instant if there is sufficientgeneration to meet demand. Power systems are designed so that if all generationis available then there will always be a positive margin; however, due to unforcedoutages at generators and varying meteorological conditions (in systems withsignificant amounts of varying renewables) there is a non-zero probability of ashortfall occurring.In this Section, we consider the structure of the full adequacy modellingapproach, as summarized in Figure 1 (with the exception of the linear regressionapproach which is considered in more detail in Section 3). A time-collapsed (or ‘snapshot’) adequacy model is designed to model thedistribution of the system margin at a randomly selected time instant duringthe peak season [28, 14]. We propose the use of an hourly time-collapsed model,where each hour of the day t is modelled separately. The key advantage of thisapproach is that the impacts of a range of demand profiles on the whole daycan be considered–this is important as some heat demand profiles peak in themorning (e.g., [29]). Using this approach, the system margin Z t for a given hour t is given by the linear sum Z t = X t + Y t − D t , (1)where X t represents dispatchable generation, Y t represents renewable genera-tion, and D t represents total system demand. (Each of the variables of (1) are5andom variables.) Dispatchable generation X t consists of conventional ther-mal plant and interconnectors, whilst renewable generation Y t is modelled as acombination of onshore wind, offshore wind, and solar generation. The ‘overall’margin Z combines the profile for the whole day, and as such can be written Z = (cid:88) t =0 I t Z t , (2)where I t is a binary variable with a value of unity if it is hour t , and is zerootherwise.It is worthwhile stressing the time dependencies in (1). Dispatchable gen-eration X t is considered to be equally likely to be available during the wholepeak demand period, and so this random variable is independent of demand andrenewables [30]. On the other hand, both renewable generation Y t and demand D t are dependent on weather, and so the distribution of net demand D t − Y t must be found by considering coincident times (i.e., these are both assumeddependent on the weather of a given time). Once the net demand has beenfound, the distribution of the system margin Z t for each hour t can be found byconvolution of the probability distribution functions of the net demand D t − Y t and conventional generation X t . The system margin Z can be used to define a range of risk metrics to un-derstand the likelihood and severity of shortfalls. The likelihood is consideredusing the Loss of Load Expectation (LOLE), having units of hrs/yr, and is givenby LOLE = E (cid:32) n − (cid:88) i =0 Pr(
Z < (cid:33) , (3)where n is the number of periods in year and E denotes the expectation operator.The LOLE metric has the advantage of being the target security standard ofmany European systems, whilst also being closely linked to the Loss of LoadProbability (LOLP), which is used as an operational indicator of scarcity bytransmission system operators.The LOLE is subsequently used to determine the Additional Capacity toSecure (ACTS). For a given security standard of T LOLE hours per year, theACTS is the (perfectly reliable) generation required to bring the LOLE to thatsecurity standard, Z (cid:48) t = X t + Y t − D t + ACTS s . t . LOLE( Z (cid:48) ) = T LOLE . (4)where we use LOLE( Z ) to denote the calculation of LOLE from (3) using systemmargin Z (cid:48) (as calculated as in (2)).For example, suppose that the GB security standard is 3 hours LOLE peryear, but the generation already committed for the τ − It is also useful to define the peak demand for a season of N Wtr . winterdays so that the peak of different demand distributions can be compared. Thiswork uses the method that is used to define Average Cold Spell peak demand[31]. This approach resamples winter demands many times to to determine thedistribution of peak demands empirically; the median value of these demandpeaks is then selected as the Peak Demand. This method can be denoted forthe time-collapsed model of this work asPeak Demand = Median (max { D , D , · · · , D N Wtr . − } ) , (5)where the i th random variable over which the max {} function is taken, D i , hasthe corresponding demand model of that hour’s margin (e.g., the 6am model isused for D , D , and so forth). The design of an effective capacity market is a challenge from both a practicaland theoretical point of view [32, 33]. The GB capacity market is regardedas a well-designed, modern market [34], although technical details continue todevelop, with annual recommendations from an independent Panel of TechnicalExperts [15].A brief overview of the design of this market is given in [35]. The TargetCapacity to Secure is calculated using a range of supply- and demand-side sen-sitivities considered around the base case, as well as system-based sensitivitiesbased on National Grid’s Future Energy (FE) Scenarios. In total, between 20and 30 sensitivities are typically considered. Based on these scenarios, the LeastWorst Regret (LWR) methodology is used to estimate the Target Capacity toSecure from all scenarios, looking to identify the generating capacity that willhave the smallest regret based on projected costs associated with oversupply(based on the net Cost of New Entry) and the costs of shortfall. The lattercosts are calculated by the Expected Energy Unserved multiplied by a mon-etary estimate of the Value of Lost Load. Cost curves for each scenario arecombined, and the aggregate least worst-regret option identified.Explicitly calculating the LWR Target Capacity to Secure is beyond thescope of the current work: suffice to say, the Target Capacity to Secure is almostentirely dependent on only the largest and smallest estimates of the ACTS [6].As such, not only is it important that calculations of ACTS have low bias,but also that the variability in forecasts for supply and demand are correctlycaptured. The Range of Capacity to Secure (RoCS) is therefore considered to7valuate the total variability across all scenarios, and is defined asRoCS = max S { ACTS( S ) } − min S { ACTS( S ) } , (6)where ACTS( S ) denotes the calculation of capacity to secure ACTS using sce-nario S . For a more detailed critical discussion on the LWR methodology see[6, Apdx. 7]. G NDM as aProxy Heat Variable
We first consider a system model with electrical demand D t which is ex-plicitly decomposed into underlying electrical demand E t and electrified spaceheating demand H t , as D t = E t + H t . (7)Given this disaggregtion, we refer to the model (7) (combined with (1)) as the Explicit system model, as heating demand is accounted for explicitly within thecalculations of system adequacy.For the purposes of this work, the Explicit model (7) will be consideredthe ground truth (for a given heat demand model H t ), to which alternativeapproaches will be considered. This is because space heating demand H t hasbeen observed to have a very different demand profile to that of underlyingelectrical demand E t , irrespective of whether the means of fulfilling that demandis by gas boilers or electric heat pumps [29, 4]. The approach therefore hasadvantages of being more closely linked to the systemic changes driven by theelectrification of heat, although a method of estimating the electrical heatingdemand H t is required. To model heating demand H t for the Explicit system model, we propose thatsuitably scaled Non Daily Metered (NDM) gas demand G NDM is used as a proxyvariable, in a similar vein to [27, 36]. NDM gas demand is largely comprisedof water and space heating demand (cooking using gas is less than 3% of totaldomestic consumption) [37], and the customer composition is largely residentialand flats/commercial properties. It does not include large industrial customers(such as gas-fired power stations), who are instead billed as part of the DailyMetered class [38].Following other works, it is assumed that the daily electrified heating demandfollows some electrified heating profile h , and that water heating demand G HW isapproximately constant throughout the year [39]. As such, the (space) heatingdemand H is calculated as an affine function of the daily NDM gas demand G NDM as H t = h t n H f Dom k COP ( G NDM − G HW ) , (8)where G HW is the (constant) daily hot water demand for gas, f Dom is the frac-tion of gas demand meeting domestic demands, k COP a system-wide coefficient8f performance, and n H is the number of customers with electrified heatingdemand. The standard approach for considering the evolution of system demand isvia the use of load duration curves. With this approach, the estimated peakdemand for a given year k Peak is forecast by some means. Once this has beendetermined, the distribution of the total demand D is calculated by linearlyscaling the electrical demand E as D = k Peak
E . (9)The model (9), combined with the system margin (1) we refer to as the
Implicit system model, as changes in heat demand are implied by the coefficient k Peak .This approach is therefore used, for example, in the methodology for modellingdemands in the GB Capacity Market [40]. For the purposes of creating Implicitmodels that are equivalent to Explicit demands in a meaningful way, k Peak ischosen so that the Peak Demands (5) are equal.The clear advantage of this approach is its conciseness: once suitable loadduration curves E have been identified, only the peak demand coefficient k Peak for a given year needs to be determined. On the other hand, it must be assumedthat the load duration curve describing the electrical demand E will not changesignificantly. As mentioned in Section 2.2, there are good reasons to think thatheat demand H t has a different distribution to electrical demand E t ; however,if changes to electrified heat demand are small, then this Implicit model mightbe preferable.To study explicitly the differences between the models, we consider the Biasin the estimates of ACTS for a given scenario S to be given byBias( S ) = ACTS Im . ( S ) − ACTS Ex . ( S ) , (10)where the subscripted ACTS Ex . , ACTS Im . are the calculations of the ACTSusing Explicit model (7) and Implicit model (9), respectively. In this way, theeffect of changes in demand profiles on the ACTS can be taken into account formodels which otherwise are identical according to their Peak Demand (5).
3. Weather-Dependent Energy System Modelling
A variety of statistical inference procedures, aimed at understanding theeffects of exogenous factors (such as weather) on energy demand, have beendeveloped by both academia and industry. To ensure that all possible effectsof increased space heating are captured, we consider the statistical inferencemethods developed by both the gas system operator, National Grid Gas, andthe electricity system operator National Grid ESO (NGESO).NGESO estimates the sensitivity of electricity demand to weather usingthe Average Cold Spell methodology [31]. This calculates the sensitivity of9ariable Description W on , W off Hourly onshore/offshore wind capacity factors S, ¯ S Solar PV capacity factor T, ¯ T Population-weighted temperature W Chill , ¯ W Chill
Population-weighted wind chill T Cold , ¯ T Cold
Population-weighted cold-spell uptick t Mon − t Sun
Binary variable for weekdays (each of Monday to Sunday) t Prd , C i , t Prd , S i i th harmonic time component (C/S as cosine/sin terms) t Sunset
Sunset time t Lin
Linear time variableˆ E Out
Out-turn peak electrical demandˆ G Out
Out-turn mean winter gas demand
Table 1: Summary of weather variables and covariates used for energy system simulation,each considered at an hourly resolution. Variables with a bar ¯( · ) average the variables for theprevious 24 hours. unrestricted system demand to weather variables. (Unrestricted system demandis defined as the sum of the transmission system demand with and demand-sideresponse, embedded generation and interconnector exports all accounted for.)From this, the ‘underlying’, non-weather sensitive demand can be estimated.The exact weather variables used are not specified, unfortunately, but by farthe most common weather variable studied in academic literature is temperature(alongside temporal variables such as day of week) [24, 41, 42, 43, 1, 2, 30, 44, 5].National Grid Gas uses the Composite Weather Variable [45] to quantify theimpacts of weather on demand. Unlike the Average Cold Spell methodology,however, many of the variables used in the Composite Weather Variable arepublic, and are described in [46]. The variables include temperature, wind chill,solar irradiance, and in future could include the effects of precipitation. Combin-ing the approaches from gas and electrical domains, a total of ten weather-basedcovariates are considered, as well as a range of temporal variables (see Table 1). Accounting for the dependencies of energy systems on weather requires anapproach to convert historic weather measurements into appropriate covariates.
Meteorological reanalyses are becoming increasingly popular for modelling ofweather within the context of energy systems. These datasets are a griddedreconstruction of past weather observations, created by combining historic ob-servations with a high-fidelity numerical model of the earth system, providinga high quality, comprehensive record of how weather and climate have changedover multiple decades. In the context of energy systems, the high spatial reso-lution allows for the climate of a region or country to be captured, as well asbeing freely available for researchers [47, 43, 48, 49]. In this work, we developthe methods described in [44, 50] for deriving weather-based covariates from theMERRA-2 reanalysis data [51]. 10n total, there are six covariates based on meteorological conditions (and afurther four averaged variables), as in Table 1. These parameters are derivedfrom the raw reanalysis data as follows: • Hourly onshore and offshore wind capacity factors W On , W Off are con-structed by modification of the method from [44], with the main stepssummarised here. The MERRA-2 reanalysis near-surface wind speedsare extrapolated using a power-law to 58.9 m and 85.5 m, based on thecapacity-weighted mean onshore and offshore turbine hub heights respec-tively (from [52]). Onshore and offshore turbine power curves from [53]are obtained using [54], with aggregated GB onshore and offshore windcapacity factors then created by considering wind farm locations from [52]for the year 2017 (Figures 2a, 2b). As in [44], this results in good accuracycompared to out-turn data [55], with Coefficient of Determination R of0.95, 0.90 and RMS error of 7.9%, 7.5% for onshore and offshore windcapacity factors respectively, when compared against 2018 daily forecastcapacity factors. • Hourly solar capacity factors S are modelled using a combination of surfacetemperature and incoming surface irradiation, as described in [44]. • Hourly temperature T and cold-weather uptick variables T Cold are calcu-lated based on population-weighted 2 meter temperatures. (The latter isused as a proxy for the Cold Weather upturn of the Composite WeatherVariable, and is intended to model increased demand at cold tempera-tures.) The cold-weather uptick is calculated as T Cold = max { T − T, } , (11)with a cold spell cut-off temperature T of 3 ◦ C, based on [56, pp. 6]. Thepopulation weighting of GB is shown in Figure 2c. • Wind chill is calculated by multiplying the population-weighted 2-metertemperature T , with respect to a wind chill temperature T WC against asimilar population-weighted 2-meter wind speed W Pop , also with respectto a threshold W WC W Chill = max { T WC − T, } × max { W Pop − W WC , } . (12)The wind chill parameters W WC , T WC are chosen as − . ◦ C,which are consistent with regional values reported in [56, pp. 6].
The goal of regression is to determine underlying sensitivity of a dependentoutput variable with respect to given input variables (covariates). Least-squareslinear regression typically achieves this goal by minimizing the square of theresiduals, with the Least Square sensitivities θ L . S . determined as θ L . S . = arg min θ (cid:107) y − θ T x (cid:107) , (13)11 a) Offshore Wind (b) Onshore Wind (c) PopulationFigure 2: The onshore and offshore wind locations (a, b) and the population weights (c) forGreat Britain, used for converting raw reanalysis weather data into wind capacity factors andweather covariates. for covariates x and output y . Unfortunately, na¨ıve Least Squares (13) canlead to over-fitting as there is no penalty on the complexity of a model, riskingreturning a model with poor predictive performance due to spurious correlations[57, Ch. 7.2]. Indeed, with the relatively large number of covariates consideredin this work, it was found that the models showed poor out-of-sample predictivecapabilities compared to within-sample fitted data.To overcome this issue, we use Lasso Regularization [57, Ch. 3]. In additionto mitigating against over-fitting, Lasso Regularization provides solutions θ Lasso that are sparse . That is, coefficients corresponding to covariates which havelittle or no impact on the output are set to zero.This is achieved by adding a regularization term α (cid:107) θ (cid:107) to the Least Squarescost function (13), with the Lasso estimate of the sensitivities θ Lasso determinedas θ Lasso ( α ) = arg min θ (cid:107) y − θ T x (cid:107) + α (cid:107) θ (cid:107) . (14)The regularization term penalizes large coefficients, having the effect of reducingthe magnitude of individual entries in θ Lasso , depending on the value of α . For α →
0, the Lasso estimate tends to the Least Squares estimate (13), and willtherefore tend to over-fit; on the other hand, for sufficiently large α , all valuesin the vector θ Lasso will be zero, under-fitting in most cases. Between these twoextremes will be an ‘optimal’ value of α , α ∗ , which will maximise the out-of-sample predictive performance (in this work Coefficient of Determination, R ,is used as a scoring function).The optimal Lasso fit θ ∗ Lasso is fitted with this value of α , i.e., θ ∗ Lasso = θ Lasso ( α ∗ ) . (15)Thus, a method is required to estimate the out-of-sample of predictive perfor-mance and subsequently determine α ∗ . α ∗ and Computational Complexity To determine the out-of-sample predictive performance, and subsequentlydetermine an optimal choice of α , we use k -fold cross-validation [57, Ch. 7.10].The approach can be briefly summarised as follows:12ariable Description Reference/data X Dispatchable generation [60, 61, 62, 63] E Unrestricted electrical system demand [64, 65, 66, 67] G NDM
NDM gas demand [68] G HW Hot water gas demand [37, 39] h Electrified heat demand profiles [23, 29, 69] k COP
System-wide heat pump COP [70, 23] n H Fraction of houses converted to space heating [71] f Dom
Domestic fraction of NDM gas demand [72, 68]
Table 2: Summary of GB system case study data sources. • k cross-validation folds are created from the k -years of data, with eachfold having one year of data for validation and k − • The sensitivity θ Lasso ( α ) is determined for a range of values of α and foreach of the k cross-validation folds. • Estimates of the mean and standard error of the prediction score ( R ) arecalculated for each value of α using the value of R calculated for each ofthe k cross-validation folds. • The value of α ∗ is chosen for which the mean prediction score is withinone standard error of the maximum value of the prediction score R . • Finally, θ ∗ Lasso is calculated from (15) (using data from all k winters).Although there is no closed-form solution to (15), the computational com-plexity of the Lasso is typically the same as ordinary Least Squares [57, Ch. 3].The scikit-learn package [58] is used for all regression calculations.
4. GB Case Study System Modelling
In this section we discuss how the energy data sources of Table 2 are usedto build and validate a generally representative model of the GB system. TheGB system is chosen for study as it has had a capacity market functioningfor several years, and because it has a very high fraction of its domestic spaceheating demand met currently met by natural gas [59].
The peak demand season for both electrical and gas systems in NorthwestEurope occurs during the winter months from November to March. Followingprior works, we study of the 20 weeks of the year following the first Sunday ofNovember, with the exception of the two weeks surrounding Christmas (thesetwo weeks have low demand and so the likelihood of shortfall is negligible)[73, 30, 74]. 13 + R X U R I W K H G D \ 3 R Z H U * : (a) Demand, D + R X U R I W K H G D \ 3 R Z H U * : (b) Net Demand, D − Y T − T − T − T − T − 3 R Z H U * : (c) Dispatchable Gen., X Figure 3: The system has a peak demand (a) is close to 60 GW, with the variability of netdemand (b) much greater due to variable renewable generation. (Plotted in (a), (b) are 10-90% deciles, as well as the 1-in-10 year quantiles, based on a 30 year hindcast of demandand renewables.) As thermal plant retirements increase, the dispatchable generation X (c)reduces. Boxplots show the 0.1, 5, 25, 50, 75, 95, and 99.9% quantiles. The underlying electrical demand E is assumed to remain steady at 19/20levels, following industry five-year forecasts [60]. To consider a rapid but credibleincrease in heat pumps in a system on top of this, as could be considered atsome point on a pathway to net-zero, we consider a rate of one million domesticinstallations per year [71].Conventional generators are represented by a two-state model, using forced-outage rates from [62, Table 1], with reported availabilities between 81% and97% for these technologies. The forecast of total installed capacity of each classof generation technology is taken from the five-year forecast [60]; following previ-ous works, these total values are then disaggregated into individual generatingunits based on unit sizes taken from National Grid’s 2013 ‘Gone Green’ sce-nario [27]. The distribution of interconnector flows are modelled with a uniformdistribution. Specifically, imports are assumed to equally likely between highand low capacity factors of the individual interconnected countries reported byNGESO [75], with flows assumed independent.With these models for interconnectors and conventional generators, the prob-ability density of the dispatchable generation X can be determined via convo-lution of all individual generators and interconnectors [27]. Boxplots of thedistribution of the resulting random variable X are shown in Figure 3c for eachdelivery year. The median of the generation X for 19/20 (discounting embed-ded generation) is 54.6 GW, compared to the previously procured capacity of52.4 GW for 20/21 as reported in capacity market reports, and is thereforeconsidered reasonably representative of the GB system.14 .1.1. Estimating Historic System Demand The estimation of total demand is challenging due increasing levels of em-bedded generation [67] and customer demand management (CDM–colloquiallyreferred to as ‘triad avoidance’, and results in up to 2.5 GW of demand-sideresponse) [65]. Embedded generation represents a range of technologies, bothdispatchable (such as small diesel generation) or renewable wind and solar gen-erators. Additionally, NGESO keeps reserves to cover the loss-of-largest-infeed,which at present has a value of 1.32 GW [66] (this effectively increases demandby the same amount).The unrestricted system demand E is therefore determined as the sum ofTransmission System Demand [64]; estimated embedded wind and solar genera-tion output [64]; estimates of remaining embedded generation [67] (assuming anavailability of 90%); and, estimates of customer demand management (providedby NGESO). The latter is assumed to run at 100% from 5-6 pm and at 40%at 4pm/7pm. Collating all data, peak demands (without weather correction)match NGESO estimates of weather-corrected peak to within 2 GW from 14/15through to 19/20 winters with mean absolute error of 1.05 GW. The closeness ofestimates gives confidence that the demand model E , like the generation model X , is also broadly representative of the GB system. The heat pump load profile h will have a large impact on results, as heatdemand H at each hour is linearly related to this profile (8). Therefore, threeheat pump profiles are considered as system-wide sensitivities, taken from lit-erature using [54], and then normalised and compared in Figure 4. The firstof these we define as our central profile C , and is taken as the cold-weatherweekday profile of Love et al [29], and is based on measured data from severalhundred UK-based heat pumps. Secondly, we consider the flat profile F , asconsidered by Eyre et al in [23] (such a profile has been reported as the de-factostandard for heat demand in [1]). Finally, we compare this against the profile P of Sansom, as described in [69], from hereon referred to as the ‘peaking’ profile.It is noted in [69] that P has been very influential in policy, even though it hasa peak higher than other estimates of half-hourly heat demand.The system-wide coefficient of performance k COP is also subject to con-siderable uncertainty. In [23], the authors estimate the value of the COP forair-source heat pumps could increase from 2.0 up to 3.0 from 2010 throughto 2050, similarly increasing from 2.5 to 4.0 for ground-source heat pumps, al-though the authors assume the COP at peak to be 0.8 times lower than this (dueto colder temperatures during peak demands). Similarly, in [70], the authorsestimate seasonal performance factors (equivalent to the COP definition usedin this work) of 1.5-2.1 for air-source heat pumps and 2.0-2.8 for ground-sourceheat pumps; again, during cold weather the performance of these systems willlikely be lower than these values. To capture the range of values and possibleimprovements in building stock during any refitting, we therefore consider aCOP range from 1.5 to 2.8, with a central estimate of 2.0.15 + R X U R I W K H G D \ 3 U R I L O H Y D O X H Q R U P D O L V H G 3 U R I L O H h C / R Y H H W D O F ( \ U H H W D O P 6 D Q V R P Figure 4: The three heat pump profiles used for sensitivity analysis. The central profile C isfrom Love et al [29]; the flat profile F is from Eyre at al [23]; and the peaking profile P ofSansom is from [69]. The fraction of NDM gas demand used by domestic customers f Dom is 79%[72, 68]. It is assumed that hot water heating demand G HW is evenly spreadthrough the year [39] and that commercial and domestic properties have a sim-ilar use of hot water. Under these assumptions, the mean hourly gas demandfor hot water is 9.9 GW throughout the year [37].
5. Results
The aim of this work is to consider how electrification of heat could impact oncapacity markets through changes in Additional Capacity to Secure. In Section5.1, we first demonstrate the Lasso Regularization approach (as described inSection 3.2), before considering how the meteorological sensitivity could evolvefor τ − We first illustrate the Lasso Regularization approach outlined in Section 3.2,considering fitting the linear model for the system demand at 6pm for τ − α ∗ is selected as the value that is within one standard errorof the maximum mean coefficient of determination from that hold-out scoring.Each vertical line indicates the value of 1 /α for which the coefficients of a given16 0 R G H O &